Many industries rely on control systems in order to control processes in specific and predictable ways. Correctly defining operating parameters and control strategies for such control systems is vital for the success of the systems, and several different techniques exist for achieving this success. It will be readily appreciated that suitable control systems are vital for a range of different industries, and that the techniques and methods to be discussed below are applicable to a wide range of processes. One example of such a process is level control of interconnected tanks. This is a common problem in many industries, such as the chemical, pharmaceutical, and food industries, the minerals processing industry, the pulp and paper industry, the oil and gas industry, and the water treatment industry. More generally, level control is important in all processes where liquids or suspensions are transformed, stocked, or separated.
A flotation circuit, for example as illustrated in FIG. 1 of the accompanying drawings, has the purpose of separating valuable minerals from worthless material. Both of which are contained in a suspension of ground ore in water (so-called pulp). The separation is achieved by exploiting the hydrophobic character of certain minerals, for example, sphalerite, an important zinc mineral. The plant is usually composed of a number of interconnected flotation cells. Intermediate storage tanks and mixing tanks may be part of such a circuit as well.
The example flotation system shown in FIG. 1 includes a series of flotation tanks. The first tank receives an input flow. The tanks are interconnected using pipes and valves. The third tank in the series has an output for waste material. Each of the tanks has an output for the separated material. The fluid level in each tank is represented by a marking line. Accordingly, the different components that have to be modeled include containers, such as a flotation cell, intermediate storage tank (in most of the cases, this refers to a pump box), and a mixing tank, connectors, meaning pipes, and outlets, sensors, such as volume flow rate, froth layer thickness or pulp level, and valve opening percentage sensors, and actuators, such as control valves, and pumps.
Precise level control of the different flotation cells is of foremost importance for flotation because the froth layer thickness, that is, the thickness of the froth layer swimming on top of the liquid pulp phase, has a significant influence on the quantity and composition of the concentrate obtained from these cells. More details as well as an introduction to the various control techniques available are disclosed in the article “Model-Predictive Control of the Froth Thickness In a Flotation Circuit”, by H. S. Foroush, S. Gaulocher, E. Gallestey, to be presented at Procemin 2009, Dec. 4, 2009, Santiago de Chile.
Model-predictive control (MPC) using a black-box model is an option for performing level control. The main drawback is the necessity of doing lengthy step tests in order to identify a plant model. These tests may require conditions close to a steady-state, which is a rare case in level control. Furthermore, once a black-box model is identified, it will not be modified during operation anymore. Therefore, it cannot account for process variations or the necessity of using a different linearization point.
Mixed logical dynamical (MLD) systems, as introduced, for example, in the article “Control of Systems Integrating Logic, Dynamics, and Constraints”, A. Bemporad and M. Morari, Automatica 35(3), 1999, pp 407-427, represent a mathematical framework for modeling systems described by interacting physical laws, logical rules, and operating constraints, generally called “hybrid systems”. MLD systems are determined or described by linear dynamic equations subject to linear mixed-integer inequalities involving both continuous, e.g., real-valued, and binary, e.g, Boolean-valued, variables. The variables include continuous and binary states x, inputs u and outputs y, as well as continuous auxiliary variables z and binary auxiliary variables δ, as described in the following equations:x(t+1)=Ax(t)+B1u(t)+B2δ(t)+B3z(t)  (Eqn. 1a)y(t)=Cx(t)+D1u(t)+D2δ(t)+D3z(t)  (Eqn. 1b)E2δ(t)+E3z(t)<=E1u(t)+E4x(t)+E5  (Eqn. 1c)
In general, the variables mentioned are vectors and A, Bi, C, Di, and Ei are matrices of suitable dimensions.
In order to be well posed, the above MLD system must be such that for any given x(t) and u(t) the values of δ(t) and z(t) are defined uniquely. Formulations or relationships as Eqns. 1 appear naturally when logical statements are written as propositional calculus expressions, or when bounds on the states are set explicitly. Among the advantages of the MLD framework is the possibility to generate automatically the matrices of MLD systems from a high-level description. MLD systems generalize a wide set of models, among which there are linear hybrid systems and even nonlinear systems whose nonlinearities can be expressed or at least suitably approximated by piecewise linear functions.
EP 1 607 809 describes the combination of arbitrarily connected MLD systems in order to model and control complex industrial systems. In EP 1 607 809, a combined model is obtained that makes use of auxiliary variables to provide the overall model. In addition, EP 1 607 809 describes the use of Model Predictive Control (MPC) using a merged MLD system. As described above, MPC is a procedure of solving an optimal-control problem, which includes system dynamics and constraints on the system output, state and input variables. The main idea of model predictive control is to use a model of the plant or process, valid at least around a certain operating point, to predict the future evolution of the system. Based on this prediction, at each time step t the controller selects a sequence of future command inputs or control signals through an on-line optimization procedure, which aims at optimizing a performance, cost or objective function, and enforces fulfillment of the constraints. Only the first sample of the optimal sequence of future command inputs is actually applied to the system at time t. At time t+1, a new sequence is evaluated to replace the previous one. This on-line re-planning provides the desired feedback control feature. Model Predictive Control can be applied for stabilizing a MLD system to an equilibrium state or to track a desired reference trajectory via feedback control.
Model predictive control (MPC) in combination with a Mixed Logical Dynamical (MLD) systems description has been used for modeling and control of processes in the utility automation and process industry. By way of example, a method of scheduling a cement production is described in the article ‘Using Model Predictive Control and Hybrid Systems for Optimal Scheduling of Industrial Processes’, by E. Gallestey et al., published in AT Automatisierungstechnik, Vol. 51, no. 6, 2003, pp. 285-293.
In order to perform the optimization, MPC requires the current state of the plant as a starting point for optimization, or at least a good estimate. In the case of complex plants, the state may be not fully observable due to a limited number of sensors or unfavorably positioned sensors. Here, state estimation is necessary in order to obtain an estimate of the plant state. Moreover, state estimation can be used independently of model predictive control, namely for other control methods or even without control at all (e.g., diagnostics, monitoring, or operator decision support).